Amelia is documenting the height of sunflower plants each week. She has determined the function to be f(x) = 3x + 3, where x represents time and f(x) represents the height of the plant. Which of the following options describes the restrictions to the domain (x) and range f(x) correctly

ADomain, nonnegative values; range, nonnegative values
BDomain, nonnegative values; range, values greater than −1
CDomain, nonnegative values; range, values less than −1
DDomain, nonnegative values; range, values greater than 3

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Among the option the on that best describes the restrictions to the domain (x) and range f(x) correctly is Domain, nonnegative values; range, values greater than 3

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pinquancaro pinquancaro · Answer 2 · 2019-06-18T04:32:38-04:00

Answer:

Option d - Domain, non-negative values; range, values greater than 3

Step-by-step explanation:

Given : Amelia is documenting the height of sunflower plants each week. She has determined the function to be \(f(x) = 3x + 3\), where x represents time and f(x) represents the height of the plant.

To find : Which of the following options describes the restrictions to the domain (x) and range f(x) correctly?

Solution :

The function given, \(f(x) = 3x + 3\)

Where, x is the time and f(x) is the height of the plant.

The domain is defined as the set of values in which function is defined.

In the function the value of x represent the time so the value of x is not negative.

So, The domain of the function is non-negative values.

Range is defined as the set of values that correspond with the domain.

Now, If x is non-negative then the minimum value of x is 0.

When x=0 → f(x)=3

Which means the range of the function is always greater than 3.

Therefore, Domain, non-negative values; range, values greater than 3.

So, Option d is correct.